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Modifiable Solid: Isosceles Triangle Cross Sections Parallel to yAxis

Modifiable Solid: Isosceles Triangle Cross Sections Parallel to yAxis
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2019-05-09 00:47
Coordinate GeometrySolid GeometryCalculusGeometric Construction
In collections GeoGebra 3D & AR: PreCalc & Calculus Resources Cross Sectional Specials (Calculus)
This example demonstrates a modifiable solid where cross-sections parallel to the yAxis are isosceles triangles with adjustable base angles. Core math concepts include solid geometry, coordinate geometry, and calculus concepts like cross-section analysis. Construction utilizes GeoGebra commands such as Intersect, Segment, Midpoint, Line, Rotate, Ray, Sphere, Polygon, Textfield, Angle, CurveCartesian, and Surface. Suitable for high school and above students to explore complex geometric solids and their cross-sectional properties.

GeoGebra Commands & Parameters

  1. Intersect(lower, h, (-8, -14)) → C
  2. Intersect(upper, h, (-8, 10.145500033808613)) → B
  3. Segment(C, B) → q
  4. Intersect(upper, q, (-8, 10.145500033808613)) → G
  5. Midpoint(C, G) → T
  6. Line(T, T + (1, 0, 0)) → l_1
  7. Rotate(C, (-α), G, l_1) → C'
  8. Ray(G, C') → f_2
  9. Rotate(G, α, C, l_1) → G'
  10. Ray(C, G') → e_1
  11. Intersect(f_2, e_1) → B_1
  12. Segment(H, I) → s_1
  13. Midpoint(s_1) → E
  14. Line(E, E + (1, 0, 0)) → r_1
  15. Rotate(I, (-α), H, r_1) → I'
  16. Ray(H, I') → b_1
  17. Rotate(H, α, I, r_1) → H'
  18. Ray(I, H') → a_1
  19. Intersect(b_1, a_1) → A_1
  20. Segment(J, K) → q_1
  21. Midpoint(q_1) → F
  22. Line(F, F + (1, 0, 0)) → c
  23. Rotate(K, (-α), J, c) → K'
  24. Ray(J, K') → p_1
  25. Rotate(J, α, K, c) → J'
  26. Ray(K, J') → m_1
  27. Intersect(m_1, p_1) → Z
  28. Line(B, D) → i
  29. Sphere(B, d) → e
  30. Polygon(C, G, B_1) → q1, f_1, g_1, n_1
  31. Segment(C, B) → p
  32. Polygon(K, J, Z) → q2, l, m, n
  33. Polygon(H, I, A_1) → q3, r, s, t
  34. Textfield(upper) → InputBox1
  35. Textfield(lower) → InputBox2
  36. Textfield(a) → InputBox3
  37. Textfield(b) → InputBox4
  38. Segment(C, G) → k_1
  39. Segment(K, Z) → f
  40. Segment(J, Z) → g
  41. Segment(A_1, I) → c_1
  42. Segment(A_1, H) → d_1
  43. Segment(C, B_1) → i_1
  44. Segment(B_1, G) → j_1
  45. Angle(G, C, B_1) → β
  46. Angle(B_1, G, C) → γ
  47. CurveCartesian(t, lower(t) + (0.5 * (upper(t) - lower(t))), ((0.5 * (upper(t) - lower(t))) * tan(α)), t, a, b) → j
  48. Surface(u, ((0.5 * (upper(u) - lower(u))) * v) + lower(u), (((0.5 * (upper(u) - lower(u))) * tan(α)) * v), u, a, b, v, 0, 1) → k
  49. Surface(u, ((0.5 * (upper(u) - lower(u))) * v) + (0.5 * (lower(u) + upper(u))), (((-0.5 * (upper(u) - lower(u))) * tan(α)) * v) + ((0.5 * (upper(u) - lower(u))) * tan(α)), u, a, b, v, 0, 1) → o